Is 6 = 2 x 3? You'll be greatly messing this up!

Calculus Level 3

k=16k(3k2k)(3k+12k+1)= ?\large \sum_{k=1}^{\infty} \frac{6^k}{(3^k-2^k)(3^{k+1}-2^{k+1})} = \ ?

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